Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

jonnymiller

  • 2 years ago

Hi all, I am still working on second derivative tests having trouble with finding the critical points. The problem is find the critical points of f(x,y)=sinx+siny+cos(x+y) for x between 0 and pie/4 and y between 0 and pie/4. Classify each as a local min, max, or saddle point. f(x,y)=sinx+siny+cos(x+y) I found the partials to be: derivative of f with respect to x = fx=cosx-sin(x+y) derivative of f with respect to y = fy=cosy-sin(x+y) I am having trouble solving the partials for 0.

  • This Question is Closed
  1. jonnymiller
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    For fx=cosx-sin(x+y)=0 fy=cosy-sin(x+y)=0 x=pie/6 y=pie/6 I did this by trial and error. Does anyone know how to solve it algebraically?

  2. bbnl1990
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    First, eliminate sin(x+y): fx-fy=0 cos(x)-cos(y)=0 cos(x)=cos(y) x=y Plug x=y to either fx or fy: fx=cos(y)-sin(y+y)=0 cos(y)=sin(2y) cos(y)=cos(pi/2-2y) y=(pi/2)-2y 3y=pi/2 y=pi/6 Since x=y, x=pi/6

  3. jonnymiller
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Very clever!! That makes a lot of sense!! It's amazing how easy it looks once you've seen it done. I have been puzzling over that one for days! Thanks!

  4. bbnl1990
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Ur welcome! :)

  5. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.